Phase Functions of Typical Lunar Surface Minerals Derived for the Hapke Model and Implications for Visible to Near-Infrared Spectral Unmixing

Laboratory spectrophotometric measurements of minerals common on the lunar surface (olivine, pyroxene, plagioclase, and ilmenite) are measured over a wavelength range of 0.4 to 2.5m to better understand the effects of the particle phase function (PF; P[g]) on the application of Hapke's radiative transfer model to reflectance spectra of lunar materials. One objective of this work is to determine if accounting for wavelength-dependent photometric effects can improve spectral estimates of mineral abundance in lunar materials, particularly that of ilmenite. We also discuss a two-step calibration method to correct for the non-Lambertian behavior and wavelength dependence of the common reference standard Spectralon. Both a two-term Legendre polynomial representation of the PF and the Henyey-Greenstein PF are examined. We use our results to apply the Hapke radiative transfer model to reflectance spectra of lab mixtures and test the effects of different PF characteristics and assumptions. Laboratory spectra indicate that ilmenite exhibits more backward scattering behavior compared with silicate minerals, which are more forward scattering. We find that the variations in PF can affect derived single-scattering albedo values and thus spectral unmixing results. Because single-scattering contribution dominates the reflectance properties of dark minerals such as ilmenite, large uncertainties in derived single-scattering albedo values can be introduced by small changes in PFs. However, it is observed that the use of a wavelength-dependent PF does not produce significant differences in spectral unmixing results for binary and ternary silicate mixtures. Plain Language Summary Olivine, pyroxene, plagioclase, and ilmenite are common minerals on the lunar surface, and knowledge on their spatial and temporal distributions can help to understand the geological evolutions of our Moon. Remote sensing reflectance spectroscopy is an important technique that can be used to identify those minerals, because their reflectance spectra have different diagnostic absorption features. Since reflectance spectra could vary with the change of illumination and viewing angles, the accurate estimation of mineral concentrations using reflectance spectra would rely on light scattering models that quantitatively describe how light is scattered from the target surface. The purpose of this study is to understand the accuracy of retrieving mineral concentrations in ilmenite-bearing mixtures using the Hapke model widely used in quantitative analysis of reflectance spectra. We measured the reflectance spectra of the more transparent olivine, pyroxene, and plagioclase and the more opaque ilmenite at different viewing angles. Using these data, we quantified the scattering properties of these four minerals. We found that ilmenite is more backscattering while the other three minerals are more forward scattering. The mixing of these dark and bright materials makes the accurate interpretation of reflectance spectra data difficult. Our results suggest that well constrained scattering properties of the component minerals and their mixtures can help improve the accuracy of mineral abundance estimations.